Instructions: Show your work, use dimensional analysis, express your answer with

Question

Instructions: Show your work, use dimensional analysis, express your answer with the appropriate significant figures, and box/circle your final answer to each question for full credit. Good luck. If it took 55 s for a 1.00 mol amount of Cl2 gas (MW = 70.906 g/mol) to effuse completely from a system. In the same system with the same conditions (temperature, pressure), if a 0.732 mol amount of F2 gas (MW = 37.997 g/mol) effuses completely from the system, how many seconds will it take for this amount of F2 to effuse? Hint: Use pms-(3RT/Mw)12 and apply Graham's law of effusion. 1.

Explanation / Answer

Answer:

We know that according to Graham's law the rate of effusion of a gas is inversely proportional to square root of the mass of its particles.

Rate of effusion ( R ) = (3RT/MW)^1/2 (where MW = molecular weight)

For Cl2 gas RCl2 = (3RT/70.906)^1/2 ( MW = 70.906g/mol = given ) -----------> (1)

Similarly for RF2    =  (3RT/37.997)^1/2   ( MW = 37.997g/mol = given )-------------> (2)

We know that  RCl2 = amount of gas/ time(sec) = 1*70.906/55 = 1.2892g/sec ------------>(3)

Simlilarly for F2 RF2 =   amount of gas/time(sec) = 0.732*37.997/ t = 27.814/t --------------> (4)

Divide equation (1)/(2)

RCl2/RF2 = ( 37.997/70.906 )^1/2 = 0.732 ---------------> (5)

Put value of RCl2 and RF2 from equation (3) and (4 )in equation (5)

So, (1.2892g/sec)/ ( 27.814/t ) = .732

=> t = (27.814*0.732) /  1.2892

=> t = 15.8 sec

F2 will take 16 second to effuse 0.732 mole amount

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